RST Field Equation Mockup with Provisional Numeric Values

Baseline Substrate Field Equation

The foundational equation governing the Reactive Substrate Theory (RST) is a nonlinear wave equation that describes the evolution of the substrate field S over time and space:

∂2t S − c2 ∇2 S + β S3 = σ(χ) · FR(∇(χ · PS))

  • Wave term: ∂2t S − c2 ∇2 S — governs propagation of substrate tension.
  • Nonlinear stiffness: β S3 — introduces amplitude-dependent elasticity and dispersion.
  • Source/coupling: σ(χ) · FR(∇(χ · PS)) — external influence or coupling to matter fields.

Numeric Mockup (Substituting Working Values)

Using provisional constants, the equation becomes:

∂2t S − (3.0 × 108)2 ∇2 S ≈ (1.5 × 1026) · m−2 · kg−1 · s2 · χ3 · σ(χ) · FR(χ · PS)

  • Effective wave speed: c ≈ 3.0 × 108 m/s
  • Stiffness parameter: β ≈ 1.5 × 1026 kg−1 · m−2 · s2
  • Background amplitude: χ ≈ 2.3 × 10−5
  • GW dispersion crossover:
    • χmthrmNL ≈ 6.0 × 10−5
    • √(χmthrmNL) ≈ 7.7 × 10−3

Compact Parameter Table

Symbol Description Provisional Value
β Nonlinear elasticity constant 1.5 × 1026 kg−1 · m−2 · s2
χ Substrate amplitude (today) 2.3 × 10−5
c Wave speed 3.0 × 108 m/s
χmthrmNL Dispersion crossover threshold 6.0 × 10−5
√(χmthrmNL) Dispersion crossover scale 7.7 × 10−3

Interpretation and Implications

  • The β S3 term introduces nonlinear stiffness, meaning the substrate becomes “stiffer” at higher amplitudes.
  • This stiffness leads to horizon-scale gravitational wave dispersion — a key testable prediction of RST.
  • The numeric mockup helps visualize the scale at which nonlinear effects become significant, especially for cosmological observations.

Usage Note

This HTML block is designed for direct use in Blogger’s HTML editor. Equations use LaTeX-style syntax and can be rendered with a math plugin or theme that supports MathJax or KaTeX. The parameter values shown are provisional and intended for visualization and refinement.

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